SOLUTION: Question#1: Find the exact value of each of the following. (Hint: you may need Angle Sum/Difference, Double Angle, or Half Angle Identities): a. cos(13pi/12) b. sin(pi/8)

Algebra ->  Test -> SOLUTION: Question#1: Find the exact value of each of the following. (Hint: you may need Angle Sum/Difference, Double Angle, or Half Angle Identities): a. cos(13pi/12) b. sin(pi/8)       Log On


   

Question 1036929: Question#1:
Find the exact value of each of the following. (Hint: you may need Angle Sum/Difference, Double Angle, or Half Angle Identities):
a. cos(13pi/12)

b. sin(pi/8)

c. tan(2X) if cosX = 5/6 and X is in Quadrant 1
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the exact value of each of the following. (Hint: you may need Angle Sum/Difference, Double Angle, or Half Angle Identities):
a. cos(13pi/12) = cos[(3pi/4 + (pi/3)] = cos(3pi/4)cos(pi/3)-sin(3pi/4)sin(pi/3)
= (-sqrt(2)/2)(1/2)) - (sqrt(2)/2)(sqrt(3)/2)
etc.
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b. sin(pi/8) = sin[(pi/4)/2] = sqrt[(1-cos(pi/4))/2] = sqrt[1-(sqrt(2)/2))/2]
= sqrt[(2-sqrt(2))/4] = sqrt[(1/2) - sqrt(2)/4]
c. tan(2t) if cos(t) = 5/6 and t is in Quadrant 1
cos = x/r, so x= 5 and r = 6
then y = sqrt[6^2-5^2] = sqrt(11)
Therefore tan(t) = y/x = sqrt(11)/5
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tan(2t) = sqrt[2tan(t)/(1-tan^2(t)] = sqrt[(2sqrt(11)/5)/(1-(11/25))]
etc.
Cheers,
Stan H.
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